We basically did it cold turkey--my daughter was like yours, and she rarely tried to climb out of the crib (she only tried once and scared herself too badly to try again) so about two weeks before her third birthday, we transitioned her into a big girl bed.
The whole week leading up to it, we would say "Five days until we get your brand new big girl bed!! Four days... etc" and she got really excited about it. She had no problems transitioning, and we took her crib apart the same day she was in the bed so she understood that this was a permanent thing.
Also, the day she was going to sleep in the bed for the first time, we wore her out (lots of time outside, a shorter afternoon nap, a much later bedtime) so she was too tired to mess around before bed, and she understood the bed was for sleeping and not to get out.
Good luck! :)